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... and Copying a Formula Notes on Copying Formulas Exercise 3: Formatting the Results Notes on Precision and Formatting Exercise 4: Displayed and Stored Values Exercise 5: Formats Get ... additional information is displayed. Note that if you need additional information about another icon you must visit the Help menu item again. (b) By default, the Standard and Formatting toolbars ... move to A3. xii A Guide to Microsoft Excel 2002 for Scientists and Engineers Information box: Boxes like this contain additional information, shortcuts, etc. The Save tool New...

Ngày tải lên: 14/08/2014, 06:22

... Integer Dim Formulastring As String, XRef As String, dummy as String Dim T As String, temp As String 'Get formula and value of cell formula (y). Formulastring = expression.Forrnula absolute. ... known-xsA{ 1 ,2,3}, 1 ,O) Using these named formulas, the formula for the first derivative becomes =3*aa*xA2+2*bb*x+cc Note the formula used for pointer. It incorporates an "implicit ... either of the following forward, backward, or central difference formulas, respectively (equations 6-1, 6-2, and 6-3). - dY N AY - Y,+l - Yl dx Ax x,+~ - x, (forward difference)...

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... and C3, respectively, and the formula for the function in cells 83 and D3. Next, the formulas that perform the binary search were entered in row 4; the formula in cell A4 calculates ... contain the initial values for XI and x2, respectively, and cells 83 and 03 contain the formula for the function. Cell A4 contains the linear interpolation formula: 148 EXCEL: NUMERICAL ... iteration ceases. The default value for Maximum Change is 0.001, which is suitable for this problem, but will not be suitable for many other problems. For a problem where the magnitude of...

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... equation.Formula End If If Left(FormulaText, 1) = "=" Then FormulaText = Mid(FormulaText, 2, 1024) FormulaText = Application.ConvertFormula(FormulaText, xlAl , xlAl , - FormulaText ... Application.lsText(equation) Then FormulaText = equation 'If in quotes, remove them. If Asc(Left(FormulaText, 1)) = 34 Then - FormulaText = Mid(FormulaText, 2, Len(Formu1aText) - 1) Else FormulaText ... current values. FormulaString(R) = Application.ConvertFormula(equations(R).Formula, - For I = 1 To N If I c> C Then FormulaString(R) = Application.Substitute( - Formula St ring...

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... TO NUMERICAL ANALYSIS FOR ELECTRICAL AND COMPUTER ENGINEERS TLFeBOOK 10 FUNCTIONAL ANALYSIS IDEAS elements of x and y are complex-valued, and a ∈ C. The metric spaces in Exam- ple 1.2 are therefore also ... floating-point arithmetic unit [i.e., digital hardware for floating-point addition and subtraction appears in Ref. 2 (see pp. 295–306)]. There is a standard IEEE format for floating- point numbers. We do not consider ... If fl[x] is the operator for chopping, then fl[x] = (±.x 1 x 2 ···x t−1 x t ) × 10 e , thus, all digits x k for k>tare forced to zero. (b) If fl[x] is the operator for rounding then it is defined...

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... approach is to use a single hop to form each (physically) long-distance link, with the signal remaining in the optical domain throughout. Since a high- performance free- space optical system can carry ... r e <r crosstalk ), it is clear that the system BER perform ance is directly controlled by the OMA. Therefore, in order to optimize BER performance, the OMA should be as large as possible. From ... and therefore the system is still under conditions for applying (3). Because of the high value of P0 max , the maxi- mum number of stages, N, has not improved and is still four. Therefore in order...

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... solution depends on the form of the input signal. The follow- ing table summarizes the form of the particular solution of a linear equation for some simple input functions: For more complicated ... (Hint: When the functional form of the homogeneous and particular solutions are the same, use the same functional form for the solutions as in the case of multiple roots for the char- acteristic ... assuming the payment per period is the same for all periods. Pb. 2.4 Use the same reasoning as for the amortization problem to write the difference equation for an individual’s savings plan. Let y(k)...

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... responses for a range of values of the circuit parameters R 1 , R, V s . However, a plot of the lines L 1 and L 2 for different values of R can also pro- vide a great deal of qualitative information ... expression is then given by: For the same message as that of Pb. 3.33 and the same carrier frequency, and assuming the modulation index a = 0.85: a. Write the expression for the modulated signal. b. ... quantities we are looking for include (1) the current I through the cir- cuit, and (2) the voltage V across the load resistor R. Using Kirchoff’s voltage law and Ohm’s law for resistance R 1 , we...

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... are called the rate equations for the number of atoms in the excited state and for the photon numbers in the cavity. These coupled equations, in their simplest forms, are given by: (4.58) (4.59) where ... iterative equations for D(k) and D2(k), as given respec- tively by Eqs. (4.16) and (4.30), and with the initial conditions for the function and its derivative. The first elements for the y, D, and ... n(0). Figure 4.8 shows the ensuing dynamics for the photon population for different values of N(0). We assumed in these simulations the following values for the parameters in the laser1 function...

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... function on I if f(c) ≥f(x) for all x ∈ I. 2. f(c) is the minimum value of the function on I if f(c) ≤ f(x) for all x ∈ I. 3. An extremum is the common designation for either the maximum value ... surfaces for the two mirrors? f. Choosing ω = ω 0 , plot a 3-D mesh of T as a function of the reflection coefficients R 1 and R 2 . Show, both graphically and numerically, that the best performance ... fsolve for finding the zeros of any function. We start with a function of one variable. The recommended sequence of steps for finding the zeros of a function is as follows: 1. Edit a function M-file for...

Ngày tải lên: 13/08/2014, 02:21

... be immediately gained if we note that this form of the phasor is exactly in the polar form of a complex number, with clear geometric interpretation for its magnitude and phase. 6.6.1 Phasor of ... solution of this ODE is a sinusoidal of the form: (6.55) Our task now is to find B c and B s that would force Eq. (6.55) to be the solution of Eq. (6.54). Therefore, we substitute this trial solution ... signals. Example 6.8 Given ten signals, the phasor of each of the form where the ampli- tude and phase for each have the functional forms write a MATLAB program to compute the resultant sum phasor. ˜˜˜ ...

Ngày tải lên: 13/08/2014, 02:21

... LLC (7.107) Repeated applications of this formula and the use of Eq. (7.86) yields: (7.108) Direct calculations show that this is also valid for l = 0 and l = 1. Therefore, the orthonormal basis functions ... element of the space. 2. There is an inner (dot) product for any two elements in the space. The definition adopted here for this inner product for functions defined in the interval t min ≤ t ≤ t max ... physics course: if a force is applied to a particle that moves by an infinitesimal distance then the infinitesimal work done by the force on the particle is the scalar product of the force by the displacement;...

Ngày tải lên: 13/08/2014, 02:21

... in MATLAB]. We leave the proof of this theorem to future courses in linear algebra. For now, the for- mula for generating the value of the determinant is given here. • The determinant of a square ... this section, we restrict our discus- sion to 2 ⊗ 2 unimodular matrices, as these form the tools for the matrix formulation of ray optics and Gaussian optics, which are two of the major sub-fields ... d = c/2, thus giving for the eigenvectors the following expressions: It is common to give the eigenvectors in the normalized form (that is, fix a and c to make thus giving for the normalized values: 8.8.2...

Ngày tải lên: 13/08/2014, 02:21

... resultant transformation from a boost with parameter φ 1 , followed by another boost with parameter φ 2 . Does this rule for composition of Lorentz transformations remind you of a similar transformation ... transformations and those discussed later. • The inversion about the origin changes the coordinates as follows: (9.1) In matrix form, this transformation can be represented by: (9.2) • For the ... these transformations. You can also see in a visually more suggestive form how each of the transformations changed the image of the original matrix, if we render the image of M and its transform in...

Ngày tải lên: 13/08/2014, 02:21

... polynomial function is an expression of the form: (S.15) where a n ≠ 0 for an n th degree polynomial. The Fundamental Theorem of Algebra states that, for the above polyno- mial, there are exactly ... See Section S.4 for more details. S.2 Quadratic Functions Parabola A quadratic parabolic function is an expression of the form: y(x) = ax 2 + bx + c where a ≠ 0 (S.2) Any x for which ax 2 ... illustrate some common techniques for find- ing the probabilities for certain events. Look around, and you will find plenty more. Example 10.1 Find the probability for getting three sixes in a roll...

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